Trigonometric ratios

Preparation and Planning

Extensive use of multi-media in this lesson really helps students to visualise the 2D / 3D aspects of each activity. Access to an overhead projector will really help bring the lesson to life, though it can also be delivered via slide projection or even a verbal description of each activity and distribution of the accompanying Student Worksheets.

Varied use of role-play, multi-media and interactive activities will ensure an engaging and memorable lesson. Indeed, much of the material used within this lesson lends itself to different topic areas and can be re-used. Contextual study will aid memory and set delivery apart from other teaching, rendering it a useful revision aid or lesson for use as closure to a Scheme of Work.

Note that the Student Worksheets feature maps with scales indicated. If the Worksheets are not printed out at 100%, the scales will be rendered inaccurate. However, students are required to calculate all distances using trigonometric ratios rather than rulers, meaning that scale should not present a problem if activities are executed as specified.

There is a News Article attached to the lesson plan that reports a real-life Search and Rescue scenario. This can be photocopied and distributed for additional information.

About the MOD Topic

In addition to its military taskings, the Royal Navy's Fleet Air Arm provides Search and Rescue cover to large sections of the United Kingdom coastline, 24 hours a day and 365 days per year, typically at 15 minutes notice. Based at RNAS Culdrose in Cornwall and Prestwick in Scotland, Royal Navy helicopters are constantly available and fly missions that are as varied as they are far-reaching. In recent months, missions have included long range medical evacuations from ships at sea, assistance to vessels in distress, cliff fallers, swimmers, divers and surfers. Additionally, several hospital-to-hospital transfers from Cornwall to other parts of the country have been flown. Often missions are international in nature - the rescue of foreign mariners, assistance to foreign flagged vessels, even recoveries in France and the Republic of Ireland.

In Scotland coverage spans southern Scotland to Edinburgh, 200 nautical miles west of the Irish coast, as far north as Ben Nevis and as far south as the Lake District. It offers a much needed service in the hazardous Highlands and the isolated Hebrides as well as providing maritime SAR (Search and Rescue) in the cruel seas off the Scottish coast. In Cornwall, coverage extends over the equally hazardous and extremely busy areas of Cornwall, the Isles of Scilly, the Western English Channel and the Southwest Approaches.

The crews of 771 Squadron (Culdrose) and HMS Gannett (Prestwick) can expect to be called to a variety of tasks at any time of the day or night. The types of tasks they can be asked to do include the following:

- convey injured sailors ashore
- search for missing divers or men overboard
- rescue crews of stricken vessels
- rescue of persons in the water
- rescue of injured and incapacitated divers
- recover climbers or walkers from remote or inaccessible areas
- transport of cliff rescue teams to scene to search for missing walkers
- aero-medical evacuation of patients from one medical facility to another
- transport of a crash team
- attending the scene of a large scale accident (e.g. rail crash) to provide an air ambulance facility
- recovery of a person pronounced dead either at the scene or subsequently at a medical facility
- transport of military personnel on compassionate grounds
- military assistance to fast jet pilots following ejection or crash.

Further Opportunities for Learning

This lesson presents a number of opportunities for Citizenship-based discussion: What responsibility should the British Coastguard and Royal Naval Search and Rescue teams have for foreign vessels? What actions should we take as civilians prior to embarking on any adventurous trip? Why might the Search and Rescue teams not always winch a victim to safety but instead confirm his / her location to the Coastguard?

Invite students to prepare their own imaginary briefing sheets on one of the following fictional situations, setting Maths questions for their peers: Kite surfer in trouble on the rocks at east end of Newquay beach (Cornwall). A Fisherman suffering a heart attack 15 miles off-shore of the Scilly Isles. RAF training aircraft performed emergency landing on-water four miles off the southern Cornish coast.

Students conduct further research into historical applications of trigonometry in shipping, including commercial and exploratory vessels as well as the Royal Navy.

Demonstrate the applications of satellite technologies to students, through either the use of avalanche transceiver, in-car navigation device or handheld GPS (Global Positioning System) device. Software permitting you may be able to demonstrate routes taken via computer programmes available.

Student worksheet answers

Download the teachers notes PDF to access the answers for this lesson.